If I was charged with unlawful possession and intoxication can I just pay my fines without going to court?

Unless the charges that you have written about are "infractions" as opposed to a "misdemeanor" you are required to appear in court and make a plea of guilty, not guilty or no contest. The problem is that from what you have written, there is a chance that if convicted you could be sentenced to jail time.

I suggest that you consult with a criminal defense attorney to represent you in the matter that you are writing about.